Reduce to lowest terms: $- \dfrac{2}{3} \div - \dfrac{4}{3} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{4}{3}$ is $- \dfrac{3}{4}$ Therefore: $ - \dfrac{2}{3} \div - \dfrac{4}{3} = - \dfrac{2}{3} \times - \dfrac{3}{4} $ $ \phantom{- \dfrac{2}{3} \times - \dfrac{3}{4}} = \dfrac{-2 \times -3}{3 \times 4} $ $ \phantom{- \dfrac{2}{3} \times - \dfrac{3}{4}} = \dfrac{6}{12} $ The numerator and denominator have a common divisor of $6$, so we can simplify: $ \dfrac{6}{12} = \dfrac{6 \div 6}{12 \div 6} = \dfrac{1}{2} $